First Law of Thermodynamics
First Law of Thermodynamics
The First Law of Thermodynamics, also known as the Law of Energy Conservation, states that energy cannot be created or destroyed in an isolated system. The total amount of energy in the universe remains constant, though it may change from one form to another.
Understanding the First Law
The First Law can be expressed in the context of a thermodynamic system, which is a defined space or quantity of matter where energy exchanges are considered. In such a system, the change in internal energy ($\Delta U$) is equal to the heat ($Q$) added to the system minus the work ($W$) done by the system on its surroundings.
Mathematically, the First Law is expressed as:
$$ \Delta U = Q - W $$
Here, $\Delta U$ is the change in internal energy, $Q$ is the heat added to the system, and $W$ is the work done by the system.
Sign Convention
- Heat (Q): Positive when heat is added to the system, negative when heat is lost from the system.
- Work (W): Positive when work is done by the surroundings on the system, negative when work is done by the system on the surroundings.
Forms of Energy
Energy can exist in various forms within a thermodynamic system:
- Kinetic Energy: Energy due to motion.
- Potential Energy: Energy due to position or composition.
- Internal Energy: Sum of all kinetic and potential energies of the particles within the system.
Applications of the First Law
The First Law can be applied in various processes, including:
- Isothermal Process: Temperature remains constant ($\Delta U = 0$).
- Adiabatic Process: No heat exchange with surroundings ($Q = 0$).
- Isobaric Process: Pressure remains constant.
- Isochoric Process: Volume remains constant ($W = 0$).
Differences and Important Points
| Aspect | Description | Example |
|---|---|---|
| Conservation of Energy | The First Law emphasizes that energy is conserved and cannot be created or destroyed. | In a closed system, the energy from burning fuel is converted into heat and work. |
| Internal Energy | Internal energy is the total energy contained within a system. | The internal energy of a gas increases when heated. |
| Heat | Heat is the transfer of energy due to a temperature difference. | Adding heat to water increases its temperature. |
| Work | Work is the transfer of energy due to a force acting over a distance. | Compressing a piston in an engine does work on the gas inside. |
| State Function | Internal energy is a state function, meaning it depends only on the current state, not on how it got there. | Whether heated slowly or quickly, the increase in a substance's internal energy is the same. |
Examples
Example 1: Heating Water
When water is heated on a stove, heat is transferred to the water ($Q$ is positive). If the pot is covered and no steam escapes, the system can be considered closed, and no work is done ($W = 0$). The increase in internal energy ($\Delta U$) is equal to the heat added.
$$ \Delta U = Q - W $$ $$ \Delta U = Q $$
Example 2: Gas Expansion
Consider a gas that expands in a cylinder by pushing a piston outward. The gas does work on the piston ($W$ is negative), and if heat is added to maintain the temperature, the internal energy change is the sum of heat added and work done.
$$ \Delta U = Q - W $$
If the process is adiabatic ($Q = 0$), the work done by the gas results in a decrease in internal energy.
$$ \Delta U = -W $$
Example 3: Isothermal Compression
During an isothermal compression of an ideal gas, the temperature remains constant. Since the internal energy of an ideal gas is a function of temperature, $\Delta U = 0$. The work done on the gas is equal to the heat removed from the system.
$$ \Delta U = Q - W $$ $$ 0 = Q - W $$ $$ Q = W $$
In summary, the First Law of Thermodynamics provides a fundamental principle that governs the conservation of energy in physical processes. It is a cornerstone of classical thermodynamics and has wide-ranging applications in science and engineering.